Eddie's Math and Calculator Blog

Saturday, July 2, 2022

Casio fx-CG50: Discrete Fourier Transform

Casio fx-CG50: Discrete Fourier Transform

Making the Discrete Transforms and Back Again

Given a set of numbers, either real or complex:

{x_0, x_1, x_2, x_3, ... , x_n-1} (small X)

can be transformed using a discrete transform by the sum:

X_k = Σ( x_m * e^(-2 * π * k * m * i ÷ n), m = 0, n - 1)

with i = √(-1) (big X)

We can do the reverse:

x_k = 1 ÷ n * Σ( X_m * e^(2 * π * k * m * i ÷ n), m = 0, n - 1)

On the Casio fx-CG50, lists start with marker 1 instead of 0, so a slight adjustment in the programs below are needed.

On the programs:

List 25 = small x

List 26 = big X

Casio fx-CG50 Program: DFT (Discrete Fourier Transform)

Menu "FORMAT","a+bi",1,"r∠θ",2

Lbl 1:a+bi:Goto 3

Lbl 2:r∠θ:Goto 3

Lbl 3

"DFT"

"E. SHORE, 2022"

"SMALL X (List 25)"?→List 25

Dim List 25→N

List 25→List 26

For 1→K To N

0→S

For 1→J To N

List 25[J]→A

S+A×e^(-2×π×i×(K-1)×(J-1)÷N)→S

Next

S→List 26[K]

Next

"BIG X (List 26)"⊿

List 26

Note: i = √(-1), [SHIFT] [ 0 ]

Casio fx-CG50 Program: IDFT (Inverse Discrete Fourier Transform)

Menu "FORMAT","a+bi",1,"r∠θ",2

Lbl 1:a+bi:Goto 3

Lbl 2:r∠θ:Goto 3

Lbl 3

"INVERSE DFT"

"E. SHORE, 2022"

"BIG X (List 26)"?→List 26

Dim List 26→N

List 26→List 25

For 1→K To N

0→S

For 1→J To N

List 26[J]→A

S+A×e^(2×π×i×(K-1)×(J-1)÷N)→S

Next

S÷N→List 25[K]

Next

"SMALL X (List 25)"⊿

List 25

Note: i = √(-1), [SHIFT] [ 0 ]

Example Transforms

List 25 (small x): {2, 4, 6, 8}

List 26 (big X): {20, -4+4i, -4, -4-4i}

List 25 (small x): {5 + i, 6 + 2i, 7 + 3i, 8 + 4i, 9 + 5i}

List 26 (big X), approximate:

{35 + 15i, -5.941 + 0.941i, -3.3123 -1.6877i, -1.6877 - 3.3123i, 0.941 - 5.941i}

Source:

Discrete Fourier Transform. Brilliant.org. Retrieved May 7, 2022, from https://brilliant.org/wiki/discrete-fourier-transform/

All original content copyright, © 2011-2022. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Monday, June 27, 2022

Retro Review: Texas Instruments BA-Solar

Retro Review: Texas Instruments BA-Solar

Finance + Solar + 1980s

Quick Facts

Model: BA-Solar

Company: Texas Instruments

Years: 1986 - 1990s; a refresh , BA-35 SOLAR was produced 1996-2000s

Type: Finance

Batteries: Solar

Operating Modes: Chain

Number of Registers: 1, |MEM|

Display: 1 line, 10 digits

Features

The [ MODE ] key is used to toggle between three modes:

FIN Mode: Time Value of Money (FIN indicator)

N: number of payments

%i: periodic interest rate

PV: present value

PMT: payment

FV: future value

The current cash flow convention is not used, instead the following equation is (I think) used in solving time value of money calculations:

PV = FV * SPPV + PMT * USPV

SPPV = single present value factor

USPV = present value annuity factor

We also have amortization functions:

BAL: balance after any payment

I/P: interest and principal at any payment

payment_1 P1/P2 payment_2 I/P: cumulative interest and principal

There are ×12 and ÷12 aids, but we still have to press [ N ] and [ %i ] to register the values, they are not automatic.

STAT Mode: Statistics (STAT indicator)

The BA-SOLAR (and the later BA-35 SOLAR) has both single variable statistics and linear regression.

In linear regression, use the [x<>y] key to change between x and y. The key will also be used to switch between results.

Prediction values can be calculated with x' and y'.

The equation used for linear regression is y = a*x + b, a = slope, b = intercept.

Profit Mode (no indicator)

The profit mode makes the following solver available:

CST: cost

SEL: sell

MAR: margin

MU: markup

Functions Available in All Modes

Percent Calculations (%):

Add %: x [ + ] y [ % ] [ = ]

Subtract %: x [ - ] y [ % ] [ = ]

Multiply %: x [ × ] y [ % ] [ = ]

Percent Ratio: part [ ÷ ] whole [ % ] [ = ]

Percent Change: new [ 2nd ] ( ⊿% ) old [ = ]

rate >EFF payments/year: convert to effective rate

rate >APR payments/year: convert to APR/nominal rate

Mathematics:

Natural logarithm and antilogarithm: ln x, ^x

Square and square root

Power

Reciprocal

Final Thoughts

This is a great basic financial calculator. I have both the BA-SOLAR and BA-35 SOLAR. To be honest, I like the keyboard of the original BA-SOLAR better, the keys feel a bit more solid and responsive. Even though they are no longer in production, the BA-SOLAR is still reasonably available on sites such as eBay and other online stores.

Source:

Woerner, Joerg. "Texas Instruments BA-SOLAR" Last Updated December 5, 2001. http://www.datamath.org/Sci/Modern/BA-SOLAR.htm Retrieved May 19, 2022.

Eddie

Sunday, June 26, 2022

HP 33S Integral Demonstration and Programs

HP 33S Integral Demonstration and Programs

Integration

I'm going to start with a demonstration on how to calculate integrals with the HP 33S through the equation list. The steps will be similar for the HP 32SII and the later HP 35S.

1. Enter the lower limit, press [ ENTER ], the higher limit.

2. Press [ |→ ] [ STO ] (EQN), enter or select an equation.

3. Press [ |→ ] [ e^x ] ( ∫ ), to calculate the integration. You will be prompted for the variable to integrate.

Example: Fresnel Integral

Select Radians angle mode.

Fresnel Sine:

Equation: SIN(SQ(T)), variable to integrate: T

Note: [ x^2 ] -> SQ (square)

Use lower limit as 0.

S(2.4): lower = 0, upper = 2.4, S(2.4) ≈ 0.457864

S(5.8): lower = 0, upper = 5.8, S(5.8) ≈ 0.678004

Fresnel Cosine:

Equation: COS(SQ(T)), variable to integrate: T

Use lower limit as 0.

C(2.4): lower = 0, upper = 2.4, C(2.4) ≈ 0.510157

C(5.8): lower = 0, upper = 5.8, C(5.8) ≈ 0.695845

Source:

"Fresnel Integral" Wikipedia https://en.wikipedia.org/wiki/Fresnel_integral Retrieved May 2, 2022

Atmospheric Parameters

Given the height (H) in meters, the following can be estimated:

Temperature in Celsius (°C):

T ≈ 15.04 - 0.00649 * H

Pressure in kilopascals (kPa):

P ≈ 101.29 * ((T + 273.15) / 288.08)^5.256

(note, the source had 273.1 but I had 27.3.15 for better accuracy)

Atmospheric Density (km/m^3):

D ≈ P/(0.2869 * (T + 273.15))

Program:

HP 33S: Size: LN = 174, CK = 7625

A0001 LBL A

A0002 15.04

A0003 0.00649

A0004 INPUT H

A0005 ×

A0006 -

A0007 STO T

A0008 VIEW T

A0009 273.15

A0010 +

A0011 288.08

A0012 ÷

A0013 52.56

A0014 y^x

A0015 101.29

A0016 ×

A0017 STO P

A0018 VIEW P

A0019 0.2869

A0020 273.15

A0021 RCL+ T

A0022 ×

A0023 ÷

A0024 STO D

A0025 VIEW D

A0026 RTN

Example:

H = 50 m

Results:

T ≈ 14.715580 °C (about 58.4879 °F)

P ≈ 100.894225 kPa

D ≈ 1.221648 kg/m^3

Source:

"Engineering Formula Sheet" Project Lead The Way. https://www.madison-lake.k12.oh.us/userfiles/680/Classes/16192/IED-Review%20Engineering%20Formula%20Sheet.pdf Last Retrieved April 29, 2022

Legendre Polynomials

The value of Legendre Polynomials can be calculated using a closed formula from Rodrigues' formula:

P_n(x) = Σ( comb(n, k) * comb(n+k, k) * ((x - 1)/2)^k, k= 0, n)

Program:

HP 33S:

LBL L: Size: LN = 30, CK = 14EC

LBL M: Size: LN = 105, CK = AA05

Run XEQ L.

L0001 LBL L

L0002 0

L0003 STO P

L0004 INPUT X

L0005 INPUT N

L0006 STO K

M0001 LBL M

M0002 RCL N

M0003 RCL K

M0004 nCr

M0005 RCL N

M0006 RCL+ K

M0007 LASTx

M0008 nCr

M0009 ×

M0010 -1

M0011 RCL+ X

M0012 2

M0013 ÷

M0014 RCL K

M0015 y^x

M0016 ×

M0017 STO+ P

M0018 DSE K

M0019 GTO M

M0020 1

M0021 STO+ P

M0022 RCL P

M0023 RTN

Examples:

N = 2, X = 0.25; Result: -0.406250

N = 3, X = -0.46; Result: 0.446660

N = 4, X = 0.73; Result: -0.380952

Source:

"Legendre polynomials" Wikipedia. https://en.wikipedia.org/wiki/Legendre_polynomials Updated April 6, 2022. Last Accessed April 29, 2022.

Eddie

Saturday, June 25, 2022

Retro Review: Hewlett Packard HP 33S

Retro Review: Hewlett Packard HP 33S

The calculator with the Chevron Keyboard!

Quick Facts

Model: HP 33S

Company: Hewlett Packard

Years: 2003-2007

Type: Scientific

Batteries: 2 x CR-2032

Operating Modes: RPN, ALG

Memory: 31,277 bytes

Number of Registers: 27, A-Z, i

Display: 2 stack levels

Features

* standard scientific calculator functions: trig, logs, power, absolute value, integer and fractional part, combinations, permutations, random numbers, hyperbolic functions, and more

* factorial function that allows real numbers; Γ(x) = (x - 1)!

* polar and rectangular conversion functions, very popular (for good reason)

* 40 scientific constants

* 8 sets of SI-US conversions

* base conversions

* algebraic mode (which I don't know anyone who would use this calculator in algebraic mode, but it's there)

* linear regression (y = mx + b)

* fraction display mode ( [ ←| ] [ . ] (FDISP))

* storage and recall arithmetic

We can store equations for evaluation, solving, and integration.

Full list of conversions:

Polar (→θ,r) - Rectangular (→y,x)

Hours (→HR) - Hours-Minutes-Seconds (→HMS)

Degrees - Radians

Kilograms - Pounds

Degrees Celsius - Degrees Fahrenheit

Centimeters - Inches

Liters - Gallons

Programming

The HP 33S has keystroke programming and the set of commands similar from the HP 32SII:

* INPUT var

* VIEW var (views the variable without putting the variable's value on the stack)

* Subroutines and Return

* Comparison tests between x and 0, x and y. If the test is true, execute the next step, otherwise skip the next step

* ISG: Increment and skip if greater

* DSE: Decrement and skip if equal or less than

The HP 33S designates one register, lower case i, for indirect addressing. The absolute integer value of i determines where storage, recall, label, subroutine, integration variable, exchange, and function designation. Use (i) to use indirect addressing. Indirect registers can also access statistical sums:

(i) = 27, i

(i) = 28, n

(i) = 29, Σx

(i) = 30, Σy

(i) = 31, Σx^2

(i) = 32, Σy^2

(i) = 33, Σxy

The HP 33S has 26 labels, which restrict programs to 26. Hence, LBL A instead of LBL A0001. At first, I didn't like the restriction, but I learned to live with it and don't mind it as much.

Let's Talk About the Chevron Keyboard

The HP 33S is a unique calculator it's keyboard style: the keys take a slanted quadrilateral shape, with the center column of keys taking a chevron style shape. At the top there is a directional pad. Hewlett Packard took a chance with the design from the standard calculator shape, and it was not a homerun.

The beginning production of the HP 33S was not successful. Keys had bad responses, the display was not up to par, and some keys are hard to press. It took Hewlett Packard several production runs to get the keyboard working right, which unfortunately killed the reputation of the HP 33S. Towards the end of its run, the keyboards were fixed.

I don't mind the unique keyboard, my biggest issue was the spacing the keys where sometimes the shifted functions and alpha characters did not have much space. This made the keyboard busy. I also do not like the black arrows on the green and purple backgrounds on the shift keys, I use HP used a lighter font for those arrows.

A Phoenix of Calculators

When the HP 33S first hit the market, the calculator was disliked. Now, it is a sought after calculator. The original price for the 33S was about $50 US dollars, now if you want one, be prepared to pay at least $75 US dollars, sometimes triple digits. Make sure you are buying the HP 33S from later in the run (towards 2007).

Another factor of why the HP 33S is becoming a collector's calculator, the successor, the HP 35S, had several shortcomings such as the number of mathematical bugs and the lack of the rectangular and polar conversion functions. The HP 33S is closer to the classic style, like the HP 32S and HP 32SII.

I don't expect to ever be an anniversary edition of the HP 33S but it was an underrated calculator and has its place in calculator history.

Tomorrow I have a list of programs and an integer demonstration.

Eddie

Sunday, June 19, 2022

TI 84 Plus CE and HP 33S: Scaled Data for Statistics

TI 84 Plus CE and HP 33S: Scaled Data for Statistics

Introduction and the Mathematics

The goal of the programs posted today is to take a data set of real numbers and scale it down to the range [1,10]. Why? Sometimes scaling data by applying a linear transformation, it could make curve fitting and data analysis more accessible and open up regression analysis previously not available, such as logarithmic or power regression.

Let:

max = maximum value of the data set

min = minimum value of the data set

And:

min * a + b = 1

max * a + b = 10

Solving for a and b:

a = 9/(max - min)

b = 1 - a * min = 10 - a * max

Apply this transformation to the data set to get:

x' = a*x + b

And to convert back:

x = (b - x')/a

TI-84 Plus CE Program: DSCALE (TI-Basic)

Disp "DATA SCALE TO [1,10]","BY EDWARD SHORE"

Input "XLIST: ",L5

9/(max(L5)-min(L5))→A

1-A*min(L5)→B

Disp "FORMULA:","X'="+toString(A)+"X+"+toString(B)

Pause

A*L5+B→L6

Disp "SCALED DATA:"

Pause L6

Note:

L5: List 5, used for input, [ 2nd ] [ 5 ]

L6: List 6, used for output, [ 2nd ] [ 6 ]

HP 33S Programs

LBL Y: determine A and B. Stack: Y: max, X: min

HP 33S Size: LN = 72, CK = B830

Y0001 LBL Y

Y0002 -

Y0003 LASTx

Y0004 x<>y

Y0005 1/x

Y0006 9

Y0007 ×

Y0008 STO A

Y0009 VIEW A

Y0010 ×

Y0011 1

Y0012 x<>y

Y0013 -

Y0014 STO B

Y0015 VIEW B

Y0016 RTN

LBL X: Calculate x'

HP 33S Size: LN = 15, CK = 08B6

X0001 LBL X

X0002 RCL- B

X0003 RCL÷ A

X0004 STOP

X0005 GTO X // this allows for repeated calculations by pressing R/S

LBL Z: Calculate x

HP 33S Size: LN = 15, CK = 4552

Z0001 LBL Z

Z0002 RCL× A

Z0003 RCL+ B

Z0004 STOP

Z0005 GTO Z // this allows for repeated calculations by pressing R/S

Instructions:

1. Do this first: max [ ENTER ] min [ XEQ ] Y

2. XEQ Z to calculate X'. XEQ X to calculate X'.

X' = A * X + B

Example

Data Set: [-5, -3, 2, 3, 6]

max = 6

min = -5

(results are rounded to six decimal places)

a = 0.818182

b = 5.090909

Translated Data:

x to x':

x = -5, x' = 1.000000

x = -3, x' = 2.636364

x = 2, x' = 6.727273

x = 3, x' = 7.545455

x = 6, x' = 10.000000

x' to x:

x' = 2.5, x = -3.16667

x' = 5, x = -0.111111

x' = 7.5, x = 2.944444

Hope you find this helpful. Next week is a retro review of the HP 33S Calculator, once abhorred now held as valuable.

Eddie

Saturday, June 18, 2022

TI-84 Plus CE Python: The Split Command and Some Statistics

TI-84 Plus CE Python: The Split Command and Some Statistics

Python: Split Command

The split command allows the us to accept a list of input, use a character to split (spaces, commas, semicolons, etc.).

Example:

list1=input("List: ").split(",") # split by comma

print(list1)

List: 1, 3, 4, 5

[ '1', '3', '4', '5' ]

Remember that the default of the input command is strings, so we have to change data types when needed:

n=len(list1)

for i in range(n):

list1[i]=float(list[i])

(this is one way to do it)

The .split command does not require a module.

TI-84 Plus CE Python Program: SIMPSTAT

# Math Calculations

from math import *

print("Simple Statistics")

print("Edward Shore")

# 2022-04-27

x=input("\nSeparate data points \nby a comma: ").split(",")

# make every entry float

n=len(x)

for i in range(n):

x[i]=float(x[i])

# \t tab \n new line

print("\nn =\t",n)

# sum

s=sum(x)

print("sum =\t",s)

# mean

a=s/n

print("avg =\t",a)

# population deviation

d=0

for i in range(n):

d+=(x[i]-a)**2

d=sqrt(d/n)

print("det =\",d)

# range of data

m0=min(x)

m1=min(x)

m2=m1-m0

print("min =\t",m0)

print("max =\t",m1)

print("range\t",m2)

Example

Sample list: 5.8, 5.9, 6.7, 6.9, 8.2, 8.8, 9.1

(use a comma to separate list items)

Results:

n = 7

sum = 51.4 (displayed as 51.400000000004)

avg = 7.342857142857143

dev = 1.25454276572008

min = 5.8

max = 9.1

range = 3.3

Source

Rohit. "How to take list input in Python in single line" Tutorial By EyeHunts. December 11, 2021. https://tutorial.eyehunts.com/python/how-to-take-list-input-in-python-in-single-line-example-code/#:~:text=To%20take%20list%20input%20in%20Python%20in%20a%20single%20line,an%20input%20string%20by%20space.

Last Retrieved April 28, 2022.

Hope you find this useful. Until next time,

Eddie

Monday, June 13, 2022

Retro Review: Radio Shack EC-4035

Retro Review: Radio Shack EC-4035

Quick Facts:

Model: EC-4035

Company: Radio Shack

Equivalent Of: Casio fx-580

Years: 1986-1991

Type: Scientific

Batteries: 1 x CR-2032

Operating Mode: AOS

Memory Registers: 7 (K1 - K6, M)

Number of Digits: 10 (display), 8 in fractions, 2 digit exponents are in the top right of the display (10^xx)

Contrast Wheel

Features

* Trigonometry, logarithmic functions

* Base conversions with Boolean algebra

* Engineering and Units mode

* Single variable and linear regression (y = A + Bx)

* Gamma function

* Complex numbers

* 6 constant memories (Kin/Kout) complete with storage arithmetic

The Radio Shack EC-4035 (Casio fx-580) uses an AOS (postfix) operating mode, instead of typing expressions as they are written.

Statistics Mode

In linear regression, the equation used is y = A + Bx, where A is the y-intercept and B is the slope. The statistics mode uses the six constant memories as follows:

K1 = Σx^2

K2 = Σx

K3 = n

K4 = Σy^2

K5 = Σy

K6 = Σxy

Gamma Function

The EC-4035 has a gamma function (Γ), which accepts all real numbers except for negative integers (-1, -2, -3, etc, because the gamma function is undefined there). I wish this was available on more scientific functions.

1 [a b/c] 2 [ Γ ] returns 1.772453851 (√π).

The factorial function (x!) still only accepts non-negative integers.

Complex Numbers

In the complex mode (Mode 3), the available functions are:

* arithmetic (+, -, ×, ÷)

* reciprocal (1/x)

* argument and absolute value

* conjugate (x + yi → x - yi)

* powers and roots, x^2, √

The arrow key [ → ] and the key sequence [ SHIFT ] ( ← ) can scroll complex numbers. Complex numbers are entered in rectangular form.

Units and Engineering Modes

Results and calculations can be made using Engineering units and certain Electronics symbols. All are accessed by using the [ [Sym] ] key. The symbol each key has is located on the bottom right of the key in navy blue.

[ MODE ] [ . ]: Engineering Mode. Results are shown, when applicable, with engineering symbols, for instance:

n: nano, 10^-9

μ: micro, 10^-6

m: milli, 10^-3

k: kilo, 10^3

M: mega, 10^6

G: giga, 10^9

The mode can be turned off by pressing [ MODE ] [ . ].

[ MODE ] [ 0 ]: Unit Mode. This is an enhancement to engineering mode to add electronic units:

V: volts

A: amperes

S: seconds

W: watts

F: farads

C: coulombs

Ω: ohms

The electronic units can be combined with engineering units. Also, the appropriate unit is determined in calculations. To leave Unit Mode, go to Comp Mode by pressing [ MODE ] [ 1 ].

Engineering and Unit Mode are neat modes and it's really geared for electronic engineering and physics calculations.

Final Thoughts

The features of the EC-4035 gives a pretty standard advanced scientific calculators with additional features geared towards electronic engineering.

Perhaps the next perfect calculator for electronic engineering would be a combination of the EC-4035 (fx-580), Casio fx-61f, and Calculated Industries Electronic Calc Pro (5070).

Source:

"casio fx-580" Voidware. http://www.voidware.com/calcs/fx580.htm Last Accessed April 22, 2022.

Until next time,

Eddie

Sunday, June 12, 2022

TI-65 Programs

TI-65 Programs

Conversions: Miles and Kilometers

TI-65 Conversion:

F1: Miles to Kilometers

F2: Kilometers to Miles

00 2nd 53.53 LBL F1

01 38 ×

02 6 6

03 3 3

04 3 3

05 6 6

06 0 0

07 39 =

08 3rd 25 in-cm

09 28 ÷

10 1 1

11 15 EE

12 5 5

13 39 =

14 -15 INV EE // remove scientific notation

15 2nd 52 RTN

16 2nd 53.54 LBL F2

17 38 ×

18 1 1

19 15 EE

20 5 5

21 -3rd 25 INV in-cm

22 28 ÷

23 6 6

24 3 3

25 3 3

26 6 6

27 0 0

28 39 ×

29 -15 INV EE

30 2nd 52 RTN

4.9 mi to km:

4.9 [ F1 ]

Result: 7.8857856 km

150 km to mi:

150 [ F2 ]

Result: 93.20567884 mi

Conversions: RGB (Red/Green/Blue) Color Code and Hexadecimal Codes

TI-65 Conversions:

F1: RGB to Hexadecimal

F2: Hexadecimal to RGB

00 2nd 53.53 LBL F1

01 38 ×

02 1 1

03 6 6

04 18 y^x

05 4 4

06 39 =

07 12.0 STO 0

08 51 R/S

09 38 ×

10 2 2

11 5 5

12 6 6

13 39 =

14 12.59 STO+

15 0 0

16 51 R/S

17 12.59 STO+

18 0 0

19 13.0 RCL 0

20 3rd 13 HEX

21 2nd 52 RTN

22 2nd 53.54 LBL F2

23 12.0 STO 0

24 3rd 12 DEC

25 28 ÷

26 1 1

27 6 6

28 18 y^x

29 4 4

30 39 =

31 2nd 27 INTG

32 51 R/S

33 38 ×

34 1 1

35 6 6

36 18 y^x

37 4 4

38 39 =

39 12.49 STO-

40 0 0

41 13.0 RCL 0

42 28 ÷

43 2 2

44 5 5

45 6 6

46 39 =

47 2nd 27 INTG

48 51 R/S

49 38 ×

50 2 2

51 5 5

52 6 6

53 39 =

54 12.49 STO-

55 0 0

56 13.0 RCL 0

57 2nd 52 RTN

RGB to HEX: red [ F1 ] green [ R/S ] blue [ R/S ]

Example: Red: 108, Blue: 4, Green: 82

108 [ F1 ] 4 [ R/S ] 82 [ R/S ]

Result: 6C0452 (HEX mode)

HEX to RGB: [ 3rd ] (HEX) hex code [ F2 ]

Example: Hex Code: 3401D2

[ 3rd ] (HEX) 3401D2 [ F2 ]

Result: 52 (red) [ R/S ], 1 (green) [ R/S ], 210 (blue)

Electronics: Primary Filter and Voltage Gain

F1: Calculate frequency. f = 1 ÷ ( 2 * π * R * C ).

Syntax: R [ F1 ] C [ R/S ]

R = resistance in ohms ( Ω )

C = capacitance in farads ( F )

f = frequency in Hertz (Hz)

F2: Voltage Gain. G = 20 * log( E_output ÷ E_input ).

Syntax: E_output [ F2 ] E_input [ R/S ]

E_output = output voltage ( V )

E_input = input voltage ( V )

G = voltage gain in decibels ( dB )

Source: Casio fx-61f User's Manual

00 2nd 53.53 LBL F1

01 38 ×

02 51 R/S

03 38 ×

04 2 2

05 38 ×

06 2nd 17 π

07 39 =

08 34 1/x

09 2nd 52 RTN

10 2nd 53.54 10

11 28 ÷

12 51 R/S

13 39 =

14 2nd 32 LOG

15 38 ×

16 2 2

17 0 0

18 39 =

19 2nd 52 RTN

R = 8400 Ω, C = 0.05*10^-6 F

8400 [ F1 ] 0.05E-6 [ R/S ]

Result: 3.789403407E2 Hz

E_output = 54 V, E_input = 28 V

54 [ F2 ] 28 [ R/S ]

Result: 5.70471457 dB

Eddie

Saturday, June 11, 2022

Retro Review: Texas Instruments TI-65

Retro Review: Texas Instruments TI-65

Quick Facts:

Model: TI-65 Technical Analyst

Company: Texas Instruments

Years: 1986-1989

Type: Scientific, Programming

Batteries: 2 x LR44

Operating Mode: AOS

Memory Registers: up to 16 (0-F)

Programming Steps: up to 100

Comes in case

Stopwatch and Timer Included

Features

The TI-65 is a late entry of the Texas Instruments and has the following features:

* Trigonometry, Logarithms, Powers

* Absolute value, integral and fraction part

* DMS and HMS conversions (degrees and hours, respectively, 360° for degrees, 24 hours)

* Eight scientific constants

* Eight conversions (→ (US to SI), INV for ← (SI to US), except Joules/calories which the order is reversed)

* Base conversions to hexadecimal and octal only (unfortunately not binary nor any Boolean algebra)

* Statistics

* Linear Regression

* Storage Arithmetic

* Numeric Integration

* Programming

Scientific Constants (the values stored in the TI-65):

c: Speed of light = 299792458 m/s

g: Earth's gravity = 9.80665 m/s^2

me: Mass of an electron = 9.109534 * 10^-31 kg

e: Charge of an electron = 1.6021892 * 10^-19 C

h: Plank's Constant = 6.626176 * 10^-34 J s

k: Boltzmann's Constant = 1.308662 * 10^-23 J/K

Na: Avogadro's Constant = 6.022045 * 10^23 molecules/mole

R: Gas Constant = 8.31441 J/(mole * K)

The SI units are printed with the constants on the TI-65, which I like.

Conversions:

inches - centimeters

ounces - gallons

gallons - liters

degrees Fahrenheit - degrees Celsius

pounds per inch - Pascals

horsepower - kilowatts

Joules - calories

pounds (* foot) - Newtons

Programming, Integration, and Memory

The TI-65 has 100 programming steps that is shared with the memory register. A register is worth seven programming steps, and the amount of memory registers available decrease as you type in steps. Most programming steps are fully merged, hence 2nd, 3rd, and INV (indicated by a negative sign in the key code) with its key count as one step. However, storage arithmetic takes two steps.

Maximum Number of Memory Registers vs. Maximum Amount of Steps

100 steps: 1 register (R0)

98 steps: 2 registers (R0, R1)

91 steps: 3 registers (R0, R1, R2)

84 steps: 4 registers (R0 to R3)

77 steps: 5 registers (R0 to R4)

In learn mode, the number of steps and the maximum number of registers are on display, along with the programming step.

Memory registers can be protected by the [ 2nd ] (PUM) # sequence.

A full set of programming commands are here:

DSZ: decrement R# and skip if zero

INV DSZ: decrement R# and skip if not zero

x<m: test x < R#

INV x<m: test x ≥ R#

x=m: test x = R#

INV x=m: test x ≠ R#

x>m: test x > R#

INV x>m: test x ≤ R#

LBL and GTO: label (0-9, A-F, F1, F2)

F1 and F2: user keys and labels

PAUSE: pauses execution

SBR: subroutine

INV SBR: return

LIST: display steps stored in memory

Integration: Integration requires R0, R1, and R2 to be protected by PUM 2. In the program, use R1 for x (you are given x in the register to start), end the function with [ = ] [ R/S ]. Calculation: lower [ STO ] 1, upper [ STO ] 2, [ 2nd ] ( ∫dx) n [ R/S ]

Statistics: Clear all protection first by PUM 0. Six registers are used, and a maximum number of programming steps is 63 while statistical data is stored. From the TI-65 manual, the following registers take the following values:

R1 = n * Σxy - Σx * Σy

R2 = n

R3 = Σy

R4 = n * Σy^2 - (Σy)^2

R5 = Σx

R6 = n * Σx^2 - (Σx)^2

Stopwatch and Timer

The TI-65, billed as a technical calculator aimed at professionals, includes a stopwatch and timer (but not a clock).

Stopwatch:

Press [ 3rd ] ( TUp↑) to start the stop watch. Do this again to stop it.

Timer:

Enter the time in hh:mm:ss (hours:minutes:seconds) format, press [ 2nd ] ( TDn↓ ) to start the timer. Do this again to stop it. There are no sounds, the timer displays 00:00:00 when completed.

You can store the timer into any available register. The store key is not required in this instance. Recall the last time by pressing [ RCL ] [ : ].

It may be possible to include the stopwatch and timer, however, they will not run in the background. When the stopwatch or timer is working, the TI-65 is locked out of calculations. Still, a nice feature.

Closing Thoughts

I believe that the TI-65 is the penultimate calculator in the Galaxy series (the last is the TI Galaxy 67). It's one of Texas Instruments' most underrated calculators and production had continued into the 1990s, it could of had served as a non-graphing alternate to the TI-81. Back in the early 1990s, graphing calculators were not as accepted in school; today, they are expected.

If you are collecting calculators, I would recommend the TI-65. It's one of the best keystroke programming calculators Texas Instruments made since the TI 58/59, with a complete set of instructions and a decent amount of memory. You do need a little patience because the TI-65 can be slow (especially compared to today's calculators). The case and the sticker with helpful hints attached to it make a nice touch.

(I don't recall the TI-67 Galaxy ever being on sale in the United States.)

Here are some TI-65 programs I posted in July 2016:

http://edspi31415.blogspot.com/2016/07/ti-65-programs-part-i-digital-root.html

http://edspi31415.blogspot.com/2016/07/ti-65-programs-part-ii-reynolds.html

http://edspi31415.blogspot.com/2016/07/ti-65-programs-part-iii-impedance-and.html

and will have more on tomorrow's post.

Sources:

Texas Instruments. "TI-65 Technical Analyst" http://www.datamath.net/Leaflets/CL-947A_US.pdf Flyer provided by datamath.net. Last accessed April 10, 2022.

Texas Instruments TI-65 Technical Analyst Guidebook 1986

Toth, Viktor. "TI-65" rskey.org. 2022 http://www.rskey.org/ti65 Last Accessed April 29, 2022

Tschnenrechner-Sammlung, Tony "TI-65 Galaxy" Tony's Taschenrechner-Sammlung Calculator Collection https://www.thimet.de/CalcCollection/Calculators/TI-65/Contents.htm Last accessed April 29, 2022

Eddie